Answer to Question #288192 in Differential Equations for Pankaj

Question

The function f(x, y) =cos √x^3 +y^3 is a homogenous function. Say true or false.

Answer 1

$$f(x, y)=\cos \sqrt{x^3+y^3}$$

$$f(kx, ky)=\cos \sqrt{(kx)^3+(ky)^3}$$

$$=\cos (k^{3/2}\sqrt{x^3+y^3})$$

Therefore the statement that the function $f(x, y)=\cos \sqrt{x^3+y^3}$ is a homogenous function is False.